Sunday, January 19, 2014

In the long run

It’s midnight, you’re at your favorite bar and the girl or guy of your dreams walks through the door. You know you need to talk to them, but immediately wonder how.  You can use that pick up line you planned a million times, you can fumble over some new line you just learned, or you throw a hail Mary and just say “Hi, I’m [insert your name nervously], and I think we should grab drinks.”

To all you young statisticians out there: don’t try any of these. The problem with statistics is, we always think about the long run; never the short run.

In statistics, we use this term “the long run,” stemming from a really nerdy concept called ”The Central Limit Theorem.”  I’ll leave the work of proving the theorem for our readers; suffice to say it basically states that if we do something enough, we will eventually get the actual permanent outcome.  

To some extent, our lives follow the central limit theorem in that our daily routines tell us what we actually do.  Think about your daily wake-up time: you set your alarm for 6:30am, but rarely actually wake up at exactly that time; some mornings you wake up at 6:35am and other mornings 6:25am.  If we took all those various wake-up times and graphed them, though, they would wind up normally distributed with the mean at 6:30am.  I’m stretching the realities of statistics slightly, but this is the basic concept.

The point here is this: our expectations are build around what is going to happen in the long run. But as the nervous person at the bar, there’s no such thing as a long run; because of time constraints this evening, a really short run is all we have.  

Some life events and decisions – like careers, friendships, and pick of our favorite foods – give us plenty of time to play out.  The sample size of these events is large, so we know if our expected value is going to return positive or negative results.  Other things, however, don’t have a long run.  It’s the championship game and your team needs 3 yards for a first down; if not, you lose the game (and your bet!).  In the long run, the average NFL team goes 2 ½ yards on that play (believe me; I’m a statistician).  But you need 3 yards, not 2 ½.  There is no long run; the whole season comes down to this short run.

I was recently at a casino, but needed to get back home for a friend’s birthday party.  Time was limited, so I couldn’t play the long run.  I took my $20, marched up to the roulette table, put it on my birthday (12 and 6), and hoped the odds would be in my favor.  If I had time to sit down and gamble, I may have hit those numbers in the long run – but I needed to leave.  Lucky for me, I wound up winning on the one hand I played!

When we have time to think about things and make informed decision, we should do what the long run dictates; when we don’t have time, just go with it.  When statistical probabilities exist, use them, but don’t fear when they’re absent.  When thinking about where you’re going to live for the next year, think through the probabilities.  If you’re picking where to go for dinner next week, think through the probabilities.  But if you’re at a bar, and the person of your dreams walks in – forget the probabilities.  In the short run, they probably don’t matter anyway.